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EXCHANGE WITH HOLLAND.

THE United States exchange with Holland at 40 cents per guilder. (20 stivers=1 guilder.)

EXAMPLES.

1. A, of Philadelphia, is indebted to B, of Amsterdam, 2975 guilders-how many dollars is it, at 40 cents per guilder?

Ans. $1190. 2. What must be paid in Boston for an invoice of goods, charged at 591 florins, 17 stivers, allowing the exchange at 40 cents per florin, or 2 cents per stiver, and advancing on it 60 per cent? Ans. $378.784.

EXCHANGE WITH HAMBURG. The United States exchange with Hamburg at 33 cents, per mark banco.

EXAMPLES.

1. Reduce 12843 marks banco to Federal money. Ans. $4281. 2. In $684, how many marks banco? Ans. 2052 marks. The exchange with Denmark and Norway is intrinsically the same as with Hamburg.

EXCHANGE WITH RUSSIA. Accounts are kept in Petersburg, &c., in rubles and copecs, reckoning 100 copees to 1 ruble.-100lbs. Petersburg weight are equal to 88.75lbs. of the United States.

EXAMPLES.

1. What will 7500 archeens of ravens-duck cost, at 14.5 rubles for 50 archeens?-required the answer in rubles and Federal Money? Ans. 2175 rubles, and $1631.25. 2. How many rubles must be received in Petersburg for a bill of 15500 guilders on Amsterdam, when the exchange is 30 stivers per ruble; and how many dollars? Ans. 10333 rubles, and $7750. EXCHANGE WITH GENOA, LEGHORN, FLORENCE, AND CORSICA.

The money of exchange are 12 denari=1 soldi; valued in the United States at $.05; 20 soldis 1 pezzo, piaster, or dollar,

EXAMPLE.

In 648 pezzos, 7 soldis, 6 denares, how much Federal money?

EXCHANGE WITH CHINA.

In this empire the denominations are, 10 caxa=1 candareen= $.0148, 10 candareens 1 mace=$.148, and 10 mace=1 tale= $1.48.

Their weights are 16 tales-1 catta=100 cattas 1 picul= 133 lb. United States. So lb. to cattas-cat. to lb.+.

EXAMPLE.

How many dollars will pay for an invoice of tea, amounting to 6446 tales? Ans. $9540.08.

SUPPLEMENT TO CUBIC MEASURE, Page 87.

EXAMPLES FOR PRACTICE.

1. In a load of bark, 15.5 feet in length, 3.8 feet in width, and 4 feet in height; required its value at 64 cents per foot, otherwise $8. per cord. Ans. $14.725. 2. Required the quantity in a cart 8 feet in length, 3 feet 9 inches in width, and 4 feet 4 inches in height.

Ans. 130 feet. 3. Suppose a cellar dug 16 feet in length, 16 feet in width, and 6 feet in depth; required the quantity of stone to inclose a wall 1 feet thick, and 6 feet in height inside of said cellar.

Ans. 21

perches. 4. In a section of the country where stone is bought and sold at 16.5 cubit feet per perch, required the number of perch in a pile 22 feet in length, 4.5 feet in width, and 6 feet 4 inches in height. Ans. 38 perches.

5. Suppose a cellar to contain 1728 cubic feet,-its length is 16 feet, and breadth 12 feet; required its depth. Ans. 9 feet. 6. Required the number of bushels of potatoes in a bin 6 feet in length, 4.5 feet in width, and 5 feet 9 inches, otherwise 5.75 feet in depth. Ans. 105.0555+=105 bu. 1pt.+ 7. If a cart contain 130 feet of bark, and is 8 feet in length, and 4 feet 4 inches in height; required the width.

Ans. 3ft. 9in.

8. If on a wharf 180 feet long, and 70 feet wide, wood be piled over its whole surface 10 feet high, except a cart road of 10 feet wide for its whole length, how many cords of wood would be on the wharf? Ans. 843.75 cords.

9. If a vessel contain 3600 cubic feet of bark upon her deck, and is 30 feet in length, and 20 feet in width; required the height. Ans. 6 feet.

10. If a man received no allowance for shortness in purchasing 8 cords of wood that were cut 3 inches too short, how many feet would he be the loser? Ans. 64 feet, or cord. 11. In 221184 solid inches, how many cords? Ans. 1 cord. 12. How many cubic yards in a ditch 625 feet long, 9 feet wide, and 3.5 feet deep? Ans. 7294 yards. 13. How many cubical inches, and how many cubical feet in a stick of timber that is 6 inches each width and depth, and 4 feet in length? 1728 cut in

of cub, it 14. Required the cubical yards in digging a canal one mile in length, 20 feet in width, and 6 feet in depth; and what the digging would cost at 6 cents per cubical yard

Ans. 23466 yards, and $1408 cost. 15. A room is 11 feet high, 21 long, and 16 feet wide; how many cubic feet of space in it? Ans. 3696 cubic feet.

CUBIC AND SQUARE MEASURE.

EXAMPLES.

1. How many solid feet are there in a marble stone 12.5 feet in length, 3.5 feet in depth, and 8 feet in breadth?

Ans. 350 cubic feet. 2. How many gallons of water in a trough, 6 feet in length, 1.5 feet in width, and .75 foot in depth? Ans. 50.114 gallons. 3. How many square feet in a board 16.5 feet long, and 1.5 feet. wide? Ans. 24.75 feet. 4. How many square feet in a stock of 15 boards, 12 feet 8 inches in length, and 13 inches wide? Ans. 205 ft.=205ft. 10in. 5. Required the surface (square feet) of a floor, 48.5 feet long, and 24.25 feet broad. Ans. 1176.125ft. or, 1176!ft. 6. A man paved a court 157 feet by 12 feet, at 3 cents per square yard: how many square yards did he pave, and what did The receive? Ans. 209 square yards=$6.28. 7. What is the solidity of a stone wall 53.5 feet long, 10.25 feet high, and 2 feet thick? Ans. 1096.75 cubic feet. 8. How many solid feet are there in a stick of timber 70 feet long, 15 inches thick, and 18 inches wide?

Ans. 131.25 cubic feet 1575 square feet.

9. What will be the cost of plastering a room at 10 cents per square yard, measures as follows, viz.-two sides 14.5 feet by 8.5 feet each, and two ends 12.5 feet by 8.5 feet each, with a deduction for a door that is 6 feet long, by 3.5 feet wide, and 4 windows 3.5 feet by 4 feet each. Ans. $4.24.

10. How many feet in a board 18 feet in length, and 16 inches wide? Ans. 24 feet. 11. Required the number of feet in a board 20 feet in length, and 1 foot wide.

12. Required the contents of a plank 30 feet in length, 22 in. in width, and 2 inches thick? Ans. 110 feet. 13. How many cubical feet in a block of marble 10 feet long, 4.5 feet wide, and 3 feet thick? Ans. 135 feet.

14. Bought a tier of wood measuring 28 feet in length, 3.75 feet wide, and 4 feet high, at $4. per cord, with a deduction of 4 feet, owing to some dotted sticks: I require the value of the wood.

Ans. $13. 15. Required the quantity and value of a load of charcoal 16 feet long, 3.5 feet wide, and 4 feet high, at 10 cents per bushel? Ans. 151.57+bu. value $15.157. 16. Required the number of books that are 7 inches long, 4.5 inches wide, and .5 inch thick, to fill a trunk that measures 35 inches long, 18 inches wide, and 15 inches deep.

Ans. 600 books.

MULTIPLICATION CONTRACTED.

Any number, from 12 to 20, can be multiplied at one operation, or one line of product.

RULE. Multiply the multiplicand by the unit figure of the multiplier, and add to the product of each multiplication that figure which stands next on the right hand of that which you multiplied; and when you have gone through the whole, add to the last figure in the multiplicand, what you have to carry, (which is the last figure of the product.)

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2. Compute the product of 16 times 2414, with ten figures, in the whole operation.

3. Multiply 24351 by 19.

Ans. 462669.

To multiply by any number of nines in one line, as 9, 99, 999, &c. RULE.-Annex as many ciphers to the multiplicand as there are nines in the multiplier, and from this number subtract the given multiplicand, and the remainder will be the answer required.

EXAMPLES.

2. What is the product of 48652 multiplied by 99999 ?

8465200000
84652

Ans. 8465115348

2. Multiply 72031 by 999?

Ans. 7131069.

The circumference of the earth being 360°, and as it performs one entire revolution in 24 hours, it is evident, that the motion of the earth, on its surface, from west to east, is

15° of motion in 1 hour of time; consequently,

1° of motion in 4 minutes of time, and

I' of motion in 4 seconds of time.

So having the longitude of two places given, we can find the difference of time: the place easterly having the time of day earlier than the place westerly.

RULE.-Multiply the difference of longitude by 4, and the product is the difference of time in minutes.

EXAMPLES.

1. Boston being 6° 40′ E. longitude from the city of Washington, when it is 12 o'clock at the city of Washington, what is the hour at Boston? Ans. 26 minutes 40 seconds past 12 o'clock. 2. Required the difference of time between New-York and Philadelphia; the difference of longitude is 1 degree, 7.25 minutes. Ans. 43 minutes.

MISCELLANEOUS EXAMPLES.

1. What decimal is that, which being multiplied by 15, the product will be .75? Ans. 05.

2. A man exchanged 70 bushels of rye, at $.92 cents per bushel, for 40 bushels of wheat at $1.375 per bushel, and received the balance in oats, at $.40 per bushel; how many bushels of oats did he receive? Ans. 23.5.

3. What premium must I pay for the insurance of my house against loss by fire, at the rate of or .005 percent., if my house be valued at $2475? Ans. $12.375. 4. If my horse and saddle are worth $84, and my horse be worth 6 times as much as my saddle, pray what is the value of my horse? Ans. $72. 5. If the floor of a square room contain 36 square yards, how many feet does it measure on each side? Ans. 18 feet.

6. How many solid inches in a brick which is 8 inches long, 4 inches wide, and 2 inches thick?

7. How many bricks in a cubic foot?

Ans. 64.

Ans. 27.

8. How many bricks will it take to build a wall 40 feet long, 12 feet high, and 1 foot thick?

Ans. 12960.

9. If a circle be 14 feet in diameter, what is its circumference? Ans. 43.9724-44.

10. If the distance through the centre of the earth, from side to side, be 7911 miles, how many miles around it?24863+1 11. What is the number of square miles on the surface of the earth, supposing its diameter 7911 miles, and its circumference 24853 miles? Ans. 196612083.

12. How many square inches of leather will cover a ball 3.5 inches in diameter?

NOTE. The area of a globe or ball is 4 times as much as the area of a circle of the same diameter, and may be found therefore, by multiplying the whole circumference by the whole diameter.

113.

Ans. by rule 1st. 38.5, and by rule 2d. 38.48,55 13. What are the solid contents of a round stick, 20 feet long, and 7 inches through; that is, the ends being 7 inches in diameter. Ans. by rule 1st. 55 cubic feet=64} square feet.

NOTE. The mean diameter of a cask (of a common curvature) may be found by adding two-thirds, or if the staves be but little curving, six-tenths of the difference between the head and bung diameters, to the head diameter.-The cask will then be reduced to a cylinder.

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